Model reduction for supersonic cavity flow using proper orthogonal decomposition(POD)and Galerkin projection

The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.

The proper orthogonal decomposition method for the Navier-Stokes equations

The proper orthogonal decomposition (POD) method for the instationary Navier-Stokes equations is considered. Several numerical approaches to evaluating the POD eigenfunctions are presented. The POD eigenfunctions are applied as a basis for a Galerkin projection of the instationary Navier-Stokes equations. And a low-dimensional ordinary differential models for fluid flows governed by the instationary Navier-Stokes equations are constructed. The numerical examples show that the method is feasible and efficient for optimal control of fluids.

Proper orthogonal decomposition analysis of coherent motions in a turbulent annular jet

A three-dimensional incompressible annular jet is simulated by the large eddy simulation(LES)method at a Reynolds number Re=8500.The time-averaged velocity field shows an asymmetric wake behind the central bluff-body although the flow geometry is symmetric.The proper orthogonal decomposition(POD)analysis of the velocity fluctuation vectors is conducted to study the flow dynamics of the wake flow.The distribution of turbulent kinetic energy across the three-dimensional POD modes shows that the first four eigenmodes each capture more than 1%of the turbulent kinetic energy,and hence their impact on the wake dynamics is studied.The results demonstrate that the asymmetric mean flow in the near-field of the annular jet is related to the first two POD modes which correspond to a radial shift of the stagnation point.The modes 3 and 4 involve the stretching or squeezing effects of the recirculation region in the radial direction.In addition,the spatial structure of these four POD eigenmodes also shows the counter-rotating vortices in the streamwise direction downstream of the flow reversal region.

基于POD和Kriging的水滴收集量快速预测方法

数值模拟手段预测翼面处水滴撞击特性通常较为耗时,为快速准确计算结冰条件下的翼面处水滴收集量,提出了基于本征正交分解和代理模型的水滴收集量快速预测方法。首先对FAR 25部附录C中连续最大结冰条件进行优化拉丁超立方采样,通过数值模拟手段获得各采样点在翼面处水滴收集量分布,从而构造样本空间。在此基础上,利用本征正交分解(Proper orthogonal decompostion,POD)方法找到表达和重构水滴收集量的本征模态以及相应的拟合系数。最后,利用Kriging模型建立样本空间中各采样点与拟合系数间的代理模型,实现翼面处水滴收集量分布的快速预测。经多组工况验证表明:该方法可较为准确地预测翼面处水滴收集量分布,其计算成本较数值模拟方法大幅降低,能够为无人机防除冰设计提供有益参考。

基于POD-αATS的油浸变压器瞬态温升降阶自适应变步长计算方法

针对油浸式电力变压器瞬态温升计算效率过低的问题,该文提出本征正交分解-αATS(proper orthogonal decomposition-adaptive time stepping based onαfactor,POD-αATS)降阶自适应变步长瞬态计算方法。首先,推导变压器绕组瞬态温升计算的有限元离散方程;其次,采用POD降阶算法改善传统瞬态计算中存在的条件数过大及方程阶数过高的问题;同时对于瞬态计算中的时间步长选择问题,提出适用于非线性问题的αATS变步长策略;然后,为验证方法的有效性,基于110 kV油浸式电力变压器绕组的基本结构建立二维八分区数值计算模型,同时将计算结果与基于110 kV绕组的温升实验结果进行对比。数值计算及实验结果表明,所提算法与全阶定步长算法在流场和温度场中的精度几乎相同,且流场计算效率提升约45倍,温度场计算效率提升约38倍,计算速度得到显著提高。这一点在温升实验中同样得到验证,说明该文所提算法的准确性、高效性及一定的工程实用性。

面向数字孪生模型应用的油浸式变压器绕组温度POD-RBFLP降阶计算方法

了解油浸式电力变压器绕组的温度情况是保证其运行稳定性的关键,也是当前针对油浸式变压器数字孪生分析的必然需求。为了快速地获得变压器绕组的稳态温度,该文提出一种基于本征正交分解(proper orthogonal decomposition,POD)和包含线性多项式的径向基函数响应面法(radial basis function response surface method including linear polynomial,RBFLP)的降阶计算模型。首先,讨论POD方法的降阶特性,并设计一种基于留一法交叉验证的自适应获得快照矩阵方法,以提高计算精度及效率;其次,采用响应面方法建立POD模态系数与绕组工况的相关关系,旨在实现通过绕组工况快速获得POD模态系数,从而跳过对降阶模型的复杂非线性计算,进而高效重构绕组温度场。相关算例表明,该方法具有较好的计算精度和效率,在50组测试工况下,与全阶计算相比,误差不超过2.5 K,且总计算时间仅为1.45 s;最后,基于110 kV变压器绕组搭建温升试验平台,试验结果表明,降阶计算结果相较于试验结果,平均计算误差不超过2 K,且单步计算时间仅为0.03 s,相较于同等规模的全阶计算,计算效率有较大幅度地提升。

包含快照选择策略的POD-QDEIM油浸式变压器绕组瞬态温升降阶算法研究及其实验验证

为了提高采用有限元方法对油浸式电力变压器绕组瞬态温升进行仿真的计算速度,该文提出一种包含快照选择策略的本征正交分解(proper orthogonal decomposition,POD)-基于列主元QR分解的离散经验插值(QR factorization-discrete empirical interpolation method,Q-DEIM)(POD-QDEIM)算法。首先,文章基于最小二乘有限元法与迎风有限元法推导绕组流热耦合计算方程;其次,通过引入POD方法,降低有限元方程阶数提高求解效率;同时提出POD自适应快照选择策略,在保证降阶模型精度的前提下,减小快照矩阵规模;随后,为了改善POD方法求解非线性问题时效率不高的劣势,文章结合基于Q-DEIM方法,通过插值的方法形成方程中的非线性项,从而提高每一时步非线性项的形成效率;最后,基于110 kV油浸式电力变压器绕组基本结构,建立了八分区分匝绕组传热模型以及绕组温升试验装置对所提算法进行验证,仿真及实验结果表明POD-QDEIM降阶算法的计算精度在工程上属于可接受范围,其计算效率较全阶计算提升了近11.72倍,说明该算法在油浸式电力变压器绕组瞬态温升快速仿真领域的工程应用价值。

A REDUCED-ORDER MFE FORMULATION BASED ON POD METHOD FOR PARABOLIC EQUATIONS

In this paper, we extend the applications of proper orthogonal decomposition （POD） method, i.e., apply POD method to a mixed finite element （MFE） formulation naturally satisfied Brezz-Babu^ka for parabolic equations, establish a reduced-order MFE formulation with lower dimensions and sufficiently high accuracy, and provide the error estimates between the reduced-order POD MFE solutions and the classical MFE solutions and the implementation of algorithm for solving reduced-order MFE formulation. Some numerical examples illustrate the fact that the results of numerical computation are consis- tent with theoretical conclusions. Moreover, it is shown that the new reduced-order MFE formulation based on POD method is feasible and efficient for solving MFE formulation for parabolic equations.

A NEW REDUCED-ORDER FVE ALGORITHM BASED ON POD METHOD FOR VISCOELASTIC EQUATIONS

A proper orthogonal decomposition （POD） technique is used to reduce the finite volume element （FVE） method for two-dimensional （2D） viscoelastic equations. A reduced-order fully discrete FVE algorithm with fewer degrees of freedom and sufficiently high accuracy based on POD method is established. The error estimates of the reduced- order fully discrete FVE solutions and the implementation for solving the reduced-order fully discrete FVE algorithm are provided. Some numerical examples are used to illus- trate that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order fully discrete FVE algorithm is one of the most effective numerical methods by comparing with corresponding numerical results of finite element formulation and finite difference scheme and that the reduced-order fully discrete FVE algorithm based on POD method is feasible and efficient for solving 2D viscoelastic equations.

Reduced-order finite element method based on POD for fractional Tricomi-type equation

The reduced-order finite element method （FEM） based on a proper orthogo- nal decomposition （POD） theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save mem- ory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element （FE） scheme is shown to be un- conditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations （FDEs）.

风力机翼型S809绕流流动特性的POD和DMD对比分析

失速时的流动分离现象对风力机叶片的气动性能有重要影响,S809作为典型水平轴风力机翼型,在临界失速攻角下气动性能会大幅降低。基于流动特征提取的非定常流场降阶模型(reduced-order model,ROM)是进一步深入了解非定常流动的重要手段。本文通过计算流体力学方法得到轻、深失速攻角下翼型的流动特征,对时变速度场进行本征正交分解(proper orthogonal decomposition,POD)和动态模态分解(dynamic mode decomposition,DMD)分析,得到轻、深失速下翼型的非定常流场信息(能量占比、模态频率等)。通过两种方法的对比,结果表明,POD和DMD方法能够准确捕捉流动过程中的非定常结构和升力主频相同的典型模态,但是POD方法由于基于能量特征,在捕捉模态时会忽略与升力主频相近但能量较小的流动结构,而基于频率特征的DMD方法能够准确获得场的演化信息(增长率、频率等)。本文研究有利于针对主频结构发展相应的流动控制方法,从而改善翼型流场情况,提高气动性能。

Reduced-order method for nuclear reactor primary circuit calculation

Accurate real-time simulations of nuclear reactor circuit systems are particularly important for system safety analysis and design.To effectively improve computational efficiency without reducing accuracy,this study establishes a thermal-hydraulics reduced-order model(ROM)for nuclear reactor circuit systems.The full-order circuit system calculation model is first established and verified and then used to calculate the thermal-hydraulic properties of the circuit system under different states as snapshots.The proper orthogonal decomposition method is used to extract the basis functions from snapshots,and the ROM is constructed using the least-squares method,effectively reducing the difficulty in constructing the ROM.A comparison between the full-order simulation and ROM prediction results of the AP1000 circuit system shows that the proposed ROM can improve computational efficiency by 1500 times while achieving a maximum relative error of 0.223%.This research develops a new direction and perspective for the digital twin modeling of nuclear reactor system circuits.

POD原理解析及在结构风工程中的几点应用

本征正交分解(POD)是压缩数据和提取随机场本质特征的有效技术。介绍了POD的基本原理及其在结构风工程研究方面的主要优点,这些优点包括仅使用少量的本征模态就可很好的重建风压场;预测风压场时可提高测压点的分辨率,根据已有的风压数据获得没有布置测压点处的风压时间序列。以双坡屋盖为例,利用风洞试验同步测量的风压数据对以上几方面基本内容进行讨论,包括风压场的重建和预测分析。通过在时域和频域与实验结果对比表明POD技术的有效性和实用性。

功能梯度材料动力学问题的POD模型降阶分析

为了快速分析非均质材料结构在复杂载荷作用下的动态响应,提出一种模型降阶方法,只需计算结构在简单均质材料情况下的动力学问题,进而用其计算结果对非均质材料结构进行分析.首先,采用结构内部任意一点处的材料参数值作为整个结构的材料参数,利用有限元分析软件计算该均质材料结构在动态载荷作用下的位移场建立数据库,该数据库包含计算模型各个节点(自由度为N)在某时间段内L个时刻的位移;其次,对数据库中的信息按照时间离散的特定方式组集成瞬像矩阵,并利用特征正交分解方法对其进行分解,得到该模型的L个特征正交基底,选取其中能反应模型主要特征的H个(其中H<L?N)作为一组最优基底,通过这组基底建立模型的低阶离散控制方程;最后,求解低阶离散微分方程组,得到功能梯度材料结构在复杂载荷作用下的位移场.文中分别给出二维和三维算例,比较了降阶模型和全阶模型计算结果,验证了该方法的有效性,并且计算效率能提高1～2个数量级.

Ritz-POD法及其在大跨度屋盖结构风振分析中的应用

目的提出在频域内分析大跨度屋盖结构风致动力响应的新方法--Ritz-POD法,克服传统Ritz向量叠加法的不足,完善Ritz向量叠加法在大跨度屋盖结构风振响应分析中的应用问题.方法将Ritz向量叠加法和本征正交分解法(POD)相结合,用POD得到脉动风压的前几阶本征模态及相应的荷载中心频率,生成考虑多荷载空间分布模式及荷载频率影响的Ritz向量.结果利用Ritz-POD法分析一单层球面网壳的风振响应表明,仅用前5阶本征模态就能较好地描述脉动风压的空间分布形式(约为70%～80%),合理确定外荷载空间分布模式的重要性要比考虑外荷载频率影响更为显著.结论用Ritz-POD法能够合理给出脉动风荷载的空间分布模式,并有效考虑外荷载频率对结构动力响应的影响,可用少量阶数的Ritz向量即可得到较准确的风振响应,显著提高了计算效率,并且该方法包含了结构的主要贡献模态.

基于POD的埋地热油管道停输再启动模拟高效算法

基于特征正交分解(POD)技术,开发了一种进行埋地热油管道正常输送、停输及再启动3个过程计算的高效算法。首先采用有限差分法和有限容积法建立基础样本,然后通过奇异值分解(SVD)算法得到管道停输后的沿线油温、土壤温度场和再启动流量基函数库,并插值得到任意计算参数条件下的谱系数,最后进行重构。该算法可在少量计算条件数值模拟的基础上,快速、准确地求解其他条件下停输再启动过程的相关参数。实际算例表明,POD模拟结果与直接数值解法相比,温度偏差在0.05℃以内,流量偏差小于3%。POD算法计算速度显著提高,单算例平均耗时小于0.1s,而数值算法单算例平均耗时约20min。

减阻水溶液槽道湍流特性POD分析

为进一步分析减阻水溶液湍流减阻机理,对质量分数为30×10-6十六烷基三甲基氯化铵(CTAC)水溶液槽道湍流减阻流动进行了实验研究,并基于本征正交分解方法研究减阻水溶液流动中减阻剂对流动结构的影响.结果表明:CTAC水溶液流动在不同雷诺数(1.5×104、2.5×104和3.5×104)下分别具有65.1%、70.0%和33.0%减阻效果;基于本征正交分解方法分析湍流脉动速度场,发现CTAC添加剂能够抑制湍流猝发过程中的低速流体的上喷及高速流体的下扫,即在一定程度上抑制了相干结构的发生及其发展过程,最终导致湍流减阻.

Ritz-POD法的原理及应用

提出一种在频域内分析大跨度屋盖结构的风振响应的Ritz-POD法。该方法用本征正交分解法(POD法)分解脉动风压场,得到占优的前几阶本征模态作为荷载的空间分布形式;根据此荷载空间分布形式生成Ritz向量,用Ritz向量直接叠加法分析结构风振响应,以解决大跨度屋盖结构多振型参与振动且高阶振型对结构响应贡献可能较大这一问题。运用该方法分析一单层球面网壳的风振响应,并与振型分解法对比,结果表明Ritz-POD法仅用少量的Ritz向量进行结构风振响应分析便可达到较高精度。

建立低阶模型的POD方法

将分析湍流拟序结构中的最佳正交分解技术运用到流动和传热问题中,并使用最佳正交分解技术建立了物理问题的低阶模型。通过对样本矩阵实施最佳正交分解得到一组特征函数。将控制方程采用Galerkin投影的方法投影到基函数所代表的空间上,从而得到原物理问题的低阶模型。计算结果表明,通过POD方法得到的低阶模型可以非常准确,并且快速地得到问题的解。

基于POD的大涡模拟入流脉动合成方法研究

针对并行计算特点,发展适用于流体并行计算的大涡模拟(Large Eddy Simulation,LES)入流脉动直接合成方法。基于特征正交分解(Proper Orthogonal Decomposition,POD)型谱表示法合成入流面主要网格点脉动风速时程,采用有限元形函数空间插值获得入流面所有网格点风速时程,采用UDF(User Defined Functions)编程实现Fluent软件平台流体并行计算时合成的脉动风速时程读入及赋值。进行B类1:500缩尺比风场内宽高比1:6的单体方形截面高层建筑非定常绕流LES计算,将数值模拟所得风剖面、风速谱及结构风压系数统计值、自谱、相干性等,与刚性模型测压风洞试验及文献数值模拟结果比较。研究表明,该合成方法可较好模拟紊流风场,预测结构风荷载具有一定精度。